But he's the guy in charge and sets the tone. I may hate the specific comic this movie is based on, but I know Supergirl isn't a drunken party girl in it, thats all on the people making the movie. The music stuff is 100% inspired by Gunn's work and approved of by him even if he's not directly responsible for it, although maybe the actual movie doesn't have a specific Gunn style needle drop even if the trailer makes it seem likely.
Also, since he had Supergirl in his movie first Gunn is almost certainly responsible for her personality, especially since he's running the DC stuff in general. Without Gunn, I don't think we're getting such a terrible version of Supergirl. I'm sure the writer/director of the movie are all on board with that version of Supergirl, but it almost certainly had to have come from Gunn first, and if nothing else he definitely approved of it.